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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (1): 111-126.doi: 10.3969/j.issn.1005-3085.2024.01.007

• • 上一篇    下一篇

低秩张量填充的循环算法

王俊霞1,2,  郭雄伟3,  王川龙1,2   

  1. 1. 太原师范学院数学与统计学院，晋中  030619;
    2. 智能优化计算与区块链技术山西省重点实验室，晋中 030619;
    3. 北京交通大学数学与统计学院，北京 100044
  • 收稿日期:2021-06-26 接受日期:2023-05-22 出版日期:2024-02-15 发布日期:2024-04-15
  • 通讯作者: 王川龙 E-mail: clwang1964@163.com
  • 基金资助:
    国家自然科学基金 (12371381)；山西省高等学校教学改革创新项目 (J2021551).

A Cyclic Algorithm for Low Rank Tensor Completion

WANG Junxia1,2,  GUO Xiongwei3,  WANG Chuanlong1,2   

  1. 1. School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619;
    2. Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Jinzhong 030619;
    3. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044
  • Received:2021-06-26 Accepted:2023-05-22 Online:2024-02-15 Published:2024-04-15
  • Contact: C. Wang. E-mail: clwang1964@163.com
  • Supported by:
    The National Natural Science Foundation of China (12371381); the Teaching Reform Project of Shanxi Province (J2021551).

PDF (PC)

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摘要：

针对张量填充问题，提出一种低秩张量填充的循环算法。以交替方向乘子法为基础，对子问题循环更新，有效地减少了算法在迭代过程中张量展开、矩阵折叠以及奇异值分解的计算花费。同时，在合理的假设条件下，给出了算法的收敛性分析。最后，通过数值实验与 HaLRTC 算法、DR-TR 算法及 LRTC-Logdet 算法的对比，验证了算法相对其它方法的有效性。

关键词: 张量填充, 循环更新, 交替方向乘子法

Abstract:

To solve the tensor completion problem, a cyclic algorithm for low rank tensor completion is proposed. Based on the alternating direction multiplier method, the sub-problem is circularly updated, which effectively reduces the cost of tensor expansion, matrix folding and singular value decomposition in the iterative process. At the same time, the convergence analysis of the algorithm is given under reasonable assumptions. Finally, the numerical experiments show that the proposed algorithm is more efficient than other algorithm.

Key words: tensor completion, circularly updating, alternating direction multiplier method

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